A FUNCTIONAL ANALYTIC PROOF OF THE LEBESGUE--DARST DECOMPOSITION THEOREM.

The aim of this paper is to give a functional analytic proof of the Lebesgue--Darst decomposition theorem [1]. We show that the decomposition of a nonnegative valued additive set function into absolutely continuous and singular parts with respect to another derives from the Riesz orthogonal decomposition theorem employed in a corresponding Hilbert space. [ABSTRACT FROM AUTHOR]